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地上有一个m行n列的方格，从坐标 [0,0] 到坐标 [m-1,n-1] 。一个机器人从坐标 [0, 0] 的格子开始移动，它每次可以向左、右、上、,"> 
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        <h1 class="title">leetcode面试题13. 机器人的运动范围</h1>
        <div class="stuff">
            <span>四月 11, 2020</span>
            

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            <h1 id="leetcode面试题13-机器人的运动范围"><a href="#leetcode面试题13-机器人的运动范围" class="headerlink" title="leetcode面试题13. 机器人的运动范围"></a>leetcode面试题13. 机器人的运动范围</h1><hr>
<blockquote>
<p>地上有一个m行n列的方格，从坐标 [0,0] 到坐标 [m-1,n-1] 。一个机器人从坐标 [0, 0] 的格子开始移动，它每次可以向左、右、上、下移动一格（不能移动到方格外），也不能进入行坐标和列坐标的数位之和大于k的格子。例如，当k为18时，机器人能够进入方格 [35, 37] ，因为3+5+3+7=18。但它不能进入方格 [35, 38]，因为3+5+3+8=19。请问该机器人能够到达多少个格子？</p>
</blockquote>
<blockquote>
<p>示例 1：<br>输入：m = 2, n = 3, k = 1<br>输出：3</p>
</blockquote>
<blockquote>
<p>示例 2：<br>输入：m = 3, n = 1, k = 0<br>输出：1<br>提示：</p>
</blockquote>
<blockquote>
<p>1 &lt;= n,m &lt;= 100<br>0 &lt;= k &lt;= 20</p>
</blockquote>
<hr>
<p>经典的dfs和bfs搜索。<br>bfs版好理解，线上bfs版、</p>
<h3 id="bfs"><a href="#bfs" class="headerlink" title="bfs"></a>bfs</h3><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">movingCount</span><span class="params">(<span class="keyword">int</span> m, <span class="keyword">int</span> n, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">int</span> count = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">int</span>[][] direction = &#123;&#123;<span class="number">0</span>,<span class="number">1</span>&#125;,&#123;<span class="number">1</span>,<span class="number">0</span>&#125;&#125;;</span><br><span class="line">        <span class="keyword">int</span>[][] visited = <span class="keyword">new</span> <span class="keyword">int</span>[m][n];</span><br><span class="line">        visited[<span class="number">0</span>][<span class="number">0</span>] = <span class="number">1</span>;</span><br><span class="line">        count = <span class="number">1</span>;</span><br><span class="line">        Queue&lt;<span class="keyword">int</span>[]&gt; queue = <span class="keyword">new</span> LinkedList&lt;&gt;();</span><br><span class="line">        queue.offer(<span class="keyword">new</span> <span class="keyword">int</span>[]&#123;<span class="number">0</span>,<span class="number">0</span>&#125;);</span><br><span class="line">        <span class="keyword">while</span> (!queue.isEmpty()) &#123;</span><br><span class="line">            <span class="keyword">int</span>[] cur = queue.poll();</span><br><span class="line">            <span class="keyword">int</span> x = cur[<span class="number">0</span>];</span><br><span class="line">            <span class="keyword">int</span> y = cur[<span class="number">1</span>];</span><br><span class="line">            <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; <span class="number">2</span>; i++) &#123;<span class="comment">//四个方向，仔细想其实两个方向右和下就够了，</span></span><br><span class="line">            <span class="comment">//只有两个方向就可以到达全部的点</span></span><br><span class="line">                <span class="keyword">int</span> nextx = x + direction[i][<span class="number">0</span>];</span><br><span class="line">                <span class="keyword">int</span> nexty = y + direction[i][<span class="number">1</span>];</span><br><span class="line">                <span class="comment">//三种情况，越界，访问过，不满足题意</span></span><br><span class="line">                <span class="keyword">if</span> (nextx &lt; <span class="number">0</span> || nexty &lt; <span class="number">0</span> || nextx &gt; m - <span class="number">1</span> || nexty &gt; n - <span class="number">1</span>) <span class="keyword">continue</span>;</span><br><span class="line">                <span class="keyword">if</span> (visited[nextx][nexty] == <span class="number">1</span>) <span class="keyword">continue</span>;</span><br><span class="line">                <span class="keyword">boolean</span> flag = judge(nextx,nexty,k);</span><br><span class="line">                <span class="keyword">if</span> (!flag) <span class="keyword">continue</span>;</span><br><span class="line">                visited[nextx][nexty] = <span class="number">1</span>;</span><br><span class="line">                queue.offer(<span class="keyword">new</span> <span class="keyword">int</span>[]&#123;nextx,nexty&#125;);</span><br><span class="line">                count++;</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> count;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">boolean</span> <span class="title">judge</span><span class="params">(<span class="keyword">int</span> nextx, <span class="keyword">int</span> nexty, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">return</span> (getSum(nextx) + getSum(nexty)) &lt;= k;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">getSum</span><span class="params">(<span class="keyword">int</span> a)</span> </span>&#123;<span class="comment">//求位数和</span></span><br><span class="line">        <span class="keyword">if</span> (a == <span class="number">0</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">return</span> a % <span class="number">10</span> + getSum(a / <span class="number">10</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h3 id="dfs"><a href="#dfs" class="headerlink" title="dfs"></a>dfs</h3><p>dfs和bfs思想差不多。</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br></pre></td><td class="code"><pre><span class="line"><span class="class"><span class="keyword">class</span> <span class="title">Solution</span> </span>&#123;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">movingCount</span><span class="params">(<span class="keyword">int</span> m, <span class="keyword">int</span> n, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        visited = <span class="keyword">new</span> <span class="keyword">int</span>[m][n];</span><br><span class="line">        <span class="keyword">return</span> dfs(<span class="number">0</span>,<span class="number">0</span>,k);</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">private</span> <span class="keyword">int</span>[][] visited;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">dfs</span><span class="params">(<span class="keyword">int</span> x, <span class="keyword">int</span> y, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">if</span> (x &lt; <span class="number">0</span> || y &lt; <span class="number">0</span> || x &gt; visited.length - <span class="number">1</span> || y &gt; visited[<span class="number">0</span>].length - <span class="number">1</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">if</span> (visited[x][y] == <span class="number">1</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">if</span> (!judge(x, y, k)) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">        visited[x][y] = <span class="number">1</span>;</span><br><span class="line">        <span class="keyword">int</span> ans = <span class="number">1</span>;<span class="comment">//自己1个节点</span></span><br><span class="line">        <span class="keyword">int</span>[][] direction = &#123;&#123;<span class="number">0</span>,<span class="number">1</span>&#125;,&#123;<span class="number">1</span>,<span class="number">0</span>&#125;,&#123;<span class="number">0</span>,-<span class="number">1</span>&#125;,&#123;-<span class="number">1</span>,<span class="number">0</span>&#125;&#125;;</span><br><span class="line">        <span class="keyword">for</span> (<span class="keyword">int</span> i = <span class="number">0</span>; i &lt; <span class="number">4</span>; i++) &#123;</span><br><span class="line">            <span class="keyword">int</span> nextx = x + direction[i][<span class="number">0</span>];</span><br><span class="line">            <span class="keyword">int</span> nexty = y + direction[i][<span class="number">1</span>];</span><br><span class="line">            ans += dfs(nextx, nexty,k);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">return</span> ans;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">boolean</span> <span class="title">judge</span><span class="params">(<span class="keyword">int</span> nextx, <span class="keyword">int</span> nexty, <span class="keyword">int</span> k)</span> </span>&#123;</span><br><span class="line">        <span class="keyword">return</span> (getSum(nextx) + getSum(nexty)) &lt;= k;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="function"><span class="keyword">public</span> <span class="keyword">int</span> <span class="title">getSum</span><span class="params">(<span class="keyword">int</span> a)</span> </span>&#123;<span class="comment">//求位数和</span></span><br><span class="line">        <span class="keyword">if</span> (a == <span class="number">0</span>) <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">return</span> a % <span class="number">10</span> + getSum(a / <span class="number">10</span>);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<p><strong>leetcode 73/100</strong></p>

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